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I thought somebody already had posted such an essay.
http://mailgate.nau.edu/cgi-bin/wa?A2=ind0007&L=phys-l&P=R27156
My impression is that electochemical cells can not be explained
at the elementary level;
How elementary? Elementary-school level? Obviously this subject is
not suitable for fourth grade. But it would be within the scope of an
ordinary modern-physics course.
they are what they are; period.
That seems like cop-out. It's just physics, after all.
[Using big words, like Gibbs
potential, QM or double layer, does not contribute to clarity
at the level of my teaching.]
Well, if you want to explain batteries in terms of 18th-century physics,
you're going to be disappointed. There is no ball-and-stick model that
explains why different metals have different work functions.
If you want to explain electrochemistry you're going to have to use the
methods (or at least the results) of modern physics in some form. ...
The work functions are different because of things like the Pauli
exclusion principle. You have a different number of fermions
in a different-sized box, so the Fermi level will be different.
Calculating things like work functions _ab initio_ is a real tour
de force, and we need not discuss the details here; it suffices
to accept the observed work function values:
Work function for aluminum: 4.2 eV
Work function for iron: 4.63 eV
Work function for nickel: 5.2 eV